Can we use MCTS without a generative model?
You either need a generative model or an emulator of the environment. In the later case you don't calculate your transitions and rewards using the model but feed your actions and states to the emulator and work with the results.

The emulator can be a black box as long as it returns the next state and the reward when provided with the current state and an action. You also need a way to identify all legal actions in a given state to build the tree.